Chiral extrapolation of hadronic vacuum polarization and isospin-breaking corrections

TL;DR

This paper combines dispersion relations and chiral perturbation theory to improve the understanding of hadronic vacuum polarization, especially isospin-breaking effects, and assesses their impact on the muon g-2 anomaly.

Contribution

It introduces a method to evaluate quark-mass dependence and isospin-breaking corrections to HVP using dispersion relations and chiral perturbation theory, including effects in the K K channel.

Findings

IB corrections are unlikely to explain the muon g-2 tension.

Enhanced IB effects near the K K threshold and phi resonance.

Updated estimates of IB corrections to HVP contribution.

Abstract

By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. In particular, we include IB effects in the $\bar K K$ channel, which are enhanced due to the proximity of the $\bar K K$ threshold and the $\phi$ resonance. The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections.